CUET UG 2025 — General Test Quantitative Reasoning

In an Arithmetic Progression (AP), each term increases or decreases by the same amount called the common difference $d$d.

The formula for any term is:

$$a_n = a + (n - 1)d$$an​=a+(n−1)d

where $a$a is the first term and $d$d is the common difference.

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The 7th term is 10 and the 9th term is 11.

From the 7th term to the 9th term, there are 2 steps in the sequence.

Change in value $= 11 - 10 = 1$=11−10=1

Number of steps $= 9 - 7 = 2$=9−7=2

Common difference:

$$d = \frac{1}{2}$$d=21​

$$d = 0.5$$d=0.5

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Using the 7th term to find the first term:

$$a_7 = a + (7 - 1)d$$a7​=a+(7−1)d

$$10 = a + 6(0.5)$$10=a+6(0.5)

$$10 = a + 3$$10=a+3

$$a = 7$$a=7

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Finding the 15th term:

$$a_{15} = a + (15 - 1)d$$a15​=a+(15−1)d

$$a_{15} = 7 + 14(0.5)$$a15​=7+14(0.5)

$$a_{15} = 7 + 7$$a15​=7+7

$$a_{15} = 14$$a15​=14

Therefore, the 15th term is $14$14.